the graph shows the distribution of the lengths (in seconds) of videos on a popular video - streaming site…

the graph shows the distribution of the lengths (in seconds) of videos on a popular video - streaming site. the distribution is approximately normal, with a mean of 264 seconds and a standard deviation of 75 seconds. sixteen percent of videos are shorter than what length? 39 seconds 114 seconds 189 seconds 339 seconds

the graph shows the distribution of the lengths (in seconds) of videos on a popular video - streaming site. the distribution is approximately normal, with a mean of 264 seconds and a standard deviation of 75 seconds. sixteen percent of videos are shorter than what length? 39 seconds 114 seconds 189 seconds 339 seconds

Answer

Explanation:

Step1: Recall the empirical rule for normal distribution

The empirical rule states that for a normal distribution:

  • Approximately (68%) of the data lies within (1) standard deviation of the mean ((\mu\pm\sigma))
  • Approximately (95%) of the data lies within (2) standard deviations of the mean ((\mu\pm2\sigma))
  • Approximately (99.7%) of the data lies within (3) standard deviations of the mean ((\mu\pm3\sigma))

The area to the left of (\mu - \sigma) is (\frac{100 - 68}{2}=16%)

Step2: Calculate the value of (\mu-\sigma)

Given (\mu = 264) seconds and (\sigma=75) seconds. We use the formula (x=\mu-\sigma) Substitute the values: (x = 264- 75) (x=189) seconds

Answer:

189 seconds